The Saupe matrix describing protein alignment in a liquid crystalline medium contains five independent elements, enabling the generation of up to five linearly independent alignment conditions. Measurement of internuclear residual dipolar couplings (RDCs) by NMR spectroscopy under these conditions, orthogonal in five-dimensional alignment space, provides access to the amplitude, asymmetry, and direction of motions of the internuclear vector. We previously demonstrated for the small protein domain GB3 (56 residues) that suitably orthogonal alignment conditions can be generated in a single liquid crystalline medium of Pf1 phage, by generating a series of conservative mutants that have negligible impact on the time-averaged backbone structure of the domain. Mutations involve changes in the charge of several solvent-exposed sidechains, as well as extension of the protein by either an N- or C-terminal His-tag peptide, commonly used for protein purification. These protein mutants map out the five-dimensional alignment space, providing unique insights into the structure and dynamics, and providing access to anisotropic parameters such as the 13C, 15N and 1H chemical shielding tensors. Rather than modifying the charge distribution to alter protein alignment, we have demonstrated that for detergent-solubilized systems it is also possible to change alignment by altering the detergent and lipid composition of the sample. Moreover, we have demonstrated that the anti-viral and anti-bacterial molecule squalamine can adopt a liquid crystalline phase suitable for protein alignment. Relatively strong alignment of the protein ubiquitin allowed the conclusion by others regarding the presence of large backbone motions on a slow (>10 ns) time scale to be re-addressed. Our newly measured RDCs in squalamine medium are largely inconsistent with the literature conclusions and point to a much narrower range of motions for regions of the protein engaged in secondary structure, whereas for loop regions the data fit well to the ensemble of conformations observed in crystallographic studies. We have developed and demonstrated new methods for obtaining experimental data sets that correspond to purely orthogonal alignment tensors, thereby removing the intrinsic correlation present between RDC values measured under a variety of alignment conditions. Application to the fusion peptide of hemagglutinin provided unique insights into its structure and internal dynamics.